To obtain the full one-loop amplitude we must combine the unitarity
cuts. One possibility is to carry this out prior to integration by
finding a single integrand with the correct unitarity cuts in all
channels [1]}. Some non-trivial examples where this
approach was implemented are high-loop computations in
super-Yang-Mills and supergravity (see
e.g. Refs. [2]}). On the other hand, in
high-multiplicity QCD calculations (see e.g. Ref. [3]}) the
cuts are usually combined after reducing to a basis of integrals. We
apply the latter approach here. We do so by promoting each cut
propagator to a Feynman propagator, and each cut to a Feynman
integral. We then use FIRE6 [4]} to reduce each
Feynman integral to the scalar integrals appearing in
Eq. (REF ). In each cut channel we only determine
coefficients of basis integrals with cuts in that channel. By
systematically evaluating each cut we determine all coefficients
except for those of integrals without kinematic dependence,
i.e. \(I_2(0)\)  and \(I_1\) . In the case of gauge theory, the
corresponding coefficients are determined by imposing the known
ultraviolet behavior of the amplitudes [5]}. Below, we
describe an analogous procedure for the case of gravitational
amplitudes.
